Exceptional sets for solutions to subelliptic equations
type: Item
instance of: scholarly article
title: Exceptional sets for solutions to subelliptic equations
zbMATH Open document ID: 0858.35026
DOI: 10.1007/BF02107326
author: S. K. Vodop'yanov
author: Irina Markina
published in: Siberian Mathematical Journal
publication date: 1997-03-23T00:00:00Z
review text: This paper deals with removable singularities for bounded solutions of the following class of nonlinear hypoelliptic equations: \[ -\sum^m_{j=1} X^*_jA_j(x,u,X_1u,\dots,X_mu)= f(x,u,X_1u,\dots,X_mu), \] where the \(C^\infty\) vector fields \(X_1,\dots,X_m\) fulfill the well-known Hörmander's conditions for hypoellipticity. Sufficient conditions for removability of the singularities of bounded solutions are proved. In a special case these conditions turn out to be necessary, too. An application to some variational problems is given. At the end of the paper it is shown that the capacity of the set on which a solution of the subelliptic equation is \(+\infty\) equals 0.
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35G20
zbMATH DE Number: 923537
zbMATH Keywords: removable singularities
zbMATH Keywords: nonlinear hypoelliptic equations
zbMATH Keywords: capacity
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 923537